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| This research uses the invariant gauge deformation to introduce the local rotation concept. This local rotation can be expressed by the asymmetrical displacement. For one-dimension deformation problems, the research shows that the traditional strain definition cannot express the true stress field for curving deformation even the deformation is infinitesimal locally. Then, using the new theory, the analytical solutions for typical loading cases are obtained. The solution is highly non-linear even for infinitesimal local deformation. Furthermore, the local solution and global solution are not independent. The non-locality for curving deformation is the main difficulty for the traditional mechanics in treating the curving deformation. This problem is overcome by the new theoretic understanding and formulation. |
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| Keywords: local rotation, deflection angular, intrinsic stretching, non-local deformation, rational mechanics |
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